{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 17\n",
    "\n",
    "# 差分\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a28f88cc-4776-4cc1-96b9-884fff1babdc",
   "metadata": {},
   "source": [
    "这段代码的目的是利用数值差分法来近似求解函数\n",
    "\n",
    "$$\n",
    "f(x) = e^{-x^2}\n",
    "$$\n",
    "\n",
    "的导数，并将这些数值解与解析解进行对比，从而评估不同差分方法的准确性和步长对误差的影响。具体而言，代码定义了三种数值差分方法：\n",
    "\n",
    "1. **中心差分法**：给出二阶精度近似导数的计算公式\n",
    "   $$\n",
    "   f'(a) \\approx \\frac{f(a + \\Delta x) - f(a - \\Delta x)}{2 \\Delta x}\n",
    "   $$\n",
    "\n",
    "2. **前向差分法**：使用一阶前向差分，计算公式为\n",
    "   $$\n",
    "   f'(a) \\approx \\frac{f(a + \\Delta x) - f(a)}{\\Delta x}\n",
    "   $$\n",
    "\n",
    "3. **后向差分法**：使用一阶后向差分，计算公式为\n",
    "   $$\n",
    "   f'(a) \\approx \\frac{f(a) - f(a - \\Delta x)}{\\Delta x}\n",
    "   $$\n",
    "\n",
    "代码首先计算了导数的解析解，并在指定的一组点上应用这三种数值方法，以观察数值结果与解析结果的吻合情况。然后，代码在不同步长 $\\Delta x$ 下，进一步探讨了这些方法对导数的估计精度。通常，随着 $\\Delta x$ 的减小，中心差分法的数值导数会更接近解析导数，而过小的步长可能会因计算精度问题而导致数值误差的增加。\n",
    "\n",
    "这段代码的核心目的是说明：数值差分法是近似求解导数的一种有效方法，尤其是在解析求导困难或不可行的情况下，但数值结果依赖于差分方法和步长的选取。中心差分法由于使用了两侧点的信息，通常能提供更高的精度。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54fe87af-e598-46a1-96c4-082f6c2c230f",
   "metadata": {},
   "source": [
    "## 导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6ea96548-c2ed-4bb2-a346-28cf0808fb41",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy.abc import x\n",
    "from sympy import latex, lambdify, diff, sin, log, exp  # 导入必要的符号计算函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abc2fae9-ed63-4b7b-aef4-6db43c7d1a95",
   "metadata": {},
   "source": [
    "## 定义数值求导函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "35716349-3d0a-4cef-9b96-bea24e200dbb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def num_diff(f, a, method, dx):  # 数值求导函数\n",
    "    if method == 'central':  # 中心差分法\n",
    "        return (f(a + dx) - f(a - dx)) / (2 * dx)\n",
    "    elif method == 'forward':  # 前向差分法\n",
    "        return (f(a + dx) - f(a)) / dx\n",
    "    elif method == 'backward':  # 后向差分法\n",
    "        return (f(a) - f(a - dx)) / dx\n",
    "    else:\n",
    "        raise ValueError(\"Method must be 'central', 'forward' or 'backward'.\")  # 错误处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8fe947c0-7ecf-4a2d-89c7-ad493c2bd7d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e^{- x^{2}}$"
      ],
      "text/plain": [
       "exp(-x**2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x = exp(-x**2)  # 定义函数 f(x) = exp(-x^2)\n",
    "f_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "01eafcdb-1355-4916-96e9-043f84e04e2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_array = np.linspace(-3, 3, 100)  # 定义 x 取值范围\n",
    "a_array = np.linspace(-2.5, 2.5, 11)  # 定义 a 的取值范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "71813970-946c-43f4-80ee-90a652f67093",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_fcn = lambdify(x, f_x)  # 将符号函数转换为数值函数\n",
    "f_x_array = f_x_fcn(x_array)  # 计算函数在 x_array 上的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b6f7dbe9-b83e-4292-8e85-be9902f34a55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 2 x e^{- x^{2}}$"
      ],
      "text/plain": [
       "-2*x*exp(-x**2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x_1_diff = diff(f_x, x)  # 计算 f(x) 的一阶导数\n",
    "f_x_1_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "62650789-e087-467c-ab43-c8414274f9a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_1_diff_fcn = lambdify(x, f_x_1_diff)  # 将导数转换为数值函数\n",
    "f_x_1_diff_array = f_x_1_diff_fcn(x_array)  # 计算导数在 x_array 上的值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "902f8806-efe4-45e6-a8d2-3089f7586a45",
   "metadata": {},
   "source": [
    "## 可视化函数和导数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f1264bc1-7485-4550-9778-133ec876f140",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3.0, 3.0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=plt.figaspect(0.5))\n",
    "ax = fig.add_subplot(2, 1, 1)\n",
    "\n",
    "ax.plot(x_array, f_x_array, '#0070C0', linewidth=1.5)  # 绘制函数 f(x)\n",
    "ax.set_ylim(np.floor(f_x_array.min()),\n",
    "            np.ceil(f_x_array.max()))  # 设置 y 轴范围\n",
    "\n",
    "ax.set_xlabel('x')  # 设置 x 轴标签\n",
    "ax.set_ylabel('f(x)')  # 设置 y 轴标签\n",
    "ax.set_xlim((x_array.min(), x_array.max()))  # 设置 x 轴范围\n",
    "ax.spines['right'].set_visible(False)  # 隐藏右边框\n",
    "ax.spines['top'].set_visible(False)  # 隐藏上边框\n",
    "\n",
    "ax = fig.add_subplot(2, 1, 2)\n",
    "\n",
    "ax.plot(x_array, f_x_1_diff_array, '#0070C0', linewidth=1.5)  # 绘制导数 f'(x)\n",
    "\n",
    "ax.set_xlabel('x')  # 设置 x 轴标签\n",
    "ax.set_ylabel('f\\'(x)')  # 设置 y 轴标签\n",
    "ax.spines['right'].set_visible(False)  # 隐藏右边框\n",
    "ax.spines['top'].set_visible(False)  # 隐藏上边框\n",
    "ax.set_xlim((x_array.min(), x_array.max()))  # 设置 x 轴范围"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef66ad65-c7b2-4ff9-865f-8dde288a3f4b",
   "metadata": {},
   "source": [
    "## 数值求导方法比较"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f9f09af3-0f23-45eb-96e7-9ed09eb44ac7",
   "metadata": {},
   "outputs": [],
   "source": [
    "dx = 0.2  # 步长\n",
    "\n",
    "diff_central = num_diff(f_x_fcn, a_array, 'central', dx)  # 中心差分法计算数值导数\n",
    "diff_forward = num_diff(f_x_fcn, a_array, 'forward', dx)  # 前向差分法计算数值导数\n",
    "diff_backward = num_diff(f_x_fcn, a_array, 'backward', dx)  # 后向差分法计算数值导数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6fda509e-4f8b-43de-845c-a80fcdd47b6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ca9f7e7aa0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(x_array, f_x_1_diff_array, '#0070C0', linewidth=1.5)  # 绘制解析导数\n",
    "\n",
    "ax.plot(a_array, diff_central, marker='.', \n",
    "        markersize=12, linestyle='none',\n",
    "        label='central')  # 绘制中心差分结果\n",
    "\n",
    "ax.plot(a_array, diff_forward, marker='>', \n",
    "        markersize=12, linestyle='none',\n",
    "        label='forward')  # 绘制前向差分结果\n",
    "\n",
    "ax.plot(a_array, diff_backward, marker='<', \n",
    "        markersize=12, linestyle='none',\n",
    "        label='backward')  # 绘制后向差分结果\n",
    "\n",
    "ax.set_xlabel('x')  # 设置 x 轴标签\n",
    "ax.set_ylabel('f\\'(x)')  # 设置 y 轴标签\n",
    "ax.spines['right'].set_visible(False)  # 隐藏右边框\n",
    "ax.spines['top'].set_visible(False)  # 隐藏上边框\n",
    "ax.set_xlim((x_array.min(), x_array.max()))  # 设置 x 轴范围\n",
    "plt.axhline(y=0, color='k', linestyle='--', linewidth=0.25)  # 添加 y=0 的参考线\n",
    "plt.legend()  # 添加图例"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4437a2b-fc77-4ff6-b1cd-44140d36e885",
   "metadata": {},
   "source": [
    "## 不同步长下的数值导数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cf314907-21a2-4ee6-a1ae-745bd79b2de1",
   "metadata": {},
   "outputs": [],
   "source": [
    "dx_array = np.linspace(0.01, 0.2, 20)  # 定义步长范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6a8a36e2-4fa7-4012-a01b-876b51b166ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1  # 求导点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e1278e8c-08b8-4a58-8d1e-49ddd8be7268",
   "metadata": {},
   "outputs": [],
   "source": [
    "diff_central = num_diff(f_x_fcn, a, 'central', dx_array)  # 中心差分法在不同步长下的导数\n",
    "diff_forward = num_diff(f_x_fcn, a, 'forward', dx_array)  # 前向差分法在不同步长下的导数\n",
    "diff_backward = num_diff(f_x_fcn, a, 'backward', dx_array)  # 后向差分法在不同步长下的导数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0752c8b2-5821-4944-b401-bc90df76c7b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_1_diff_a = f_x_1_diff_fcn(a)  # 解析导数在 a 处的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e8fd90af-cf22-43d8-be84-426de27b76d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, \"f'(x)\")"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(dx_array, diff_central, linewidth=1.5, \n",
    "        marker='.', label='central')  # 绘制中心差分结果\n",
    " \n",
    "ax.plot(dx_array, diff_forward, linewidth=1.5, \n",
    "        marker='>', label='forward')  # 绘制前向差分结果\n",
    " \n",
    "ax.plot(dx_array, diff_backward, linewidth=1.5, \n",
    "        marker='<', label='backward')  # 绘制后向差分结果\n",
    "\n",
    "plt.axhline(y=f_x_1_diff_a, color='k', linestyle='--', \n",
    "            linewidth=0.25, label='analytical')  # 绘制解析解参考线\n",
    "\n",
    "ax.set_xlim((dx_array.min(), dx_array.max()))  # 设置 x 轴范围\n",
    "ax.spines['right'].set_visible(False)  # 隐藏右边框\n",
    "ax.spines['top'].set_visible(False)  # 隐藏上边框\n",
    "plt.legend()  # 添加图例\n",
    "ax.set_xlabel('\\u0394x')  # 设置 x 轴标签\n",
    "ax.set_ylabel('f\\'(x)')  # 设置 y 轴标签"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
